The triangles are congruent because all three sides are congruent. (SSS) AB is congruent to CD AD is congruent to BC AC is congruent to AC

The triangles are congruent because all three sides are congruent. (SSS) AB is congruent to CD AD is congruent to BC AC is congruent to AC

Percentage question (answer)

Because we know that the total weight of the feed is 60 pounds, we can call the weight of one of the feeds x and the other 60-x. Let's say x is the blue nag feed. Then... Protein in blue nag = 0.17x Protein in green pasture = 0.25 (60-x) = 15 - 0.25x Total...

There are 52 cards, of which 13 are clubs. So the probability of drawing a club is 13/52 = 0.25 = 25%.

Use the formula V = P * e ^ rt, where V = final value, P = principal, e = 2.71828..., r = annual percentage rate compounded continuously, and t = time in years. 1.125 = 0.900 * e ^ rt Divide both sides by 0.900. 1.25 = e ^ rt So we know the final...

s = liters saccharine, w = liters of water. s / (s + w) = 0.45 s + w = 89. We then add x additional liters of water. s / (s + w + x) = 0.40. Cross-multiply. s = 0.45 (s + w) s = 0.40 (s + w + x) Because both equations are equal to s they must be equal to each other. 0.45 (s + w) = 0.40 (s +...

Word Problem (answer)

If a number is 128 percent too high, that means it is 228 percent of the actual number. So set up a ratio and cross multiply. 9120 / 228 = x / 100 912000 = 228x x = 4000

Probability (answer)

Assuming the die is fair, past rolls do not matter. There are six sides, and four of them are greater than 2. The probability is 4/6 or 2/3.

How many possible answers are there? (answer)

Think about it. There is one way (1234) to choose four out of four, four ways (123, 124, 134, 234) to choose three out of four, six ways (12, 13, 14, 23, 24, 34) to choose two out of four, and four ways (1, 2, 3, 4) to choose one out of four. Fifteen possible combinations in all. You...

We know that s + r = 17, and that 5s + 7r = 111. Express either variable in terms of the other, for example, s = 17 - r. Then substitute into second equation. So 5 (17 - r) + 7r = 111 85 - 5r + 7r = 111 2r = 26 r...

We can use the quadratic formula. 6x^2 + 11x = 2 6x^2 + 11x - 2 = 0 -11 +/- square root of (11^2 - 4*4*(-2)) / (2*6) -11 +/- square root of (121 + 48) / 12 -11 +/- square root of 169 / 12 (-11...

We know the two runners are closing at a combined rate of 12mph and that the trail is 8 miles long. So the runners will meet after 8/12 hour = 2/3 hour = 40 minutes. Check: In 2/3 of an hour, runner 1 will cover 3 1/3 miles and runner 2 will cover 4 2/3 miles. 3...

Math Word Problem (answer)

Scores are x and x + 9 x + 9 = 56% of total and x = 44% Set up a proportion and cross-multiply: x / 44 = (x + 9) / 56 56x = 44 (x + 9) 56x = 44x + 396 12x = 396 x = 33 So...

Shorter leg = x Longer leg = 3x + 3 Hypotenuse = 3x + 4 x^2 + (3x + 3)^2 = (3x + 4)^2 x^2 + (9x^2 + 18x + 9) = (9x^2 + 24x + 16) x^2 - 6x - 7 = 0 (x - 7)(x + 1) = 0 x = 7 or -1 Disregard...

What's the question?

Use the distance formula (Pythagorean theorem) to calculate the distances between each point and the center point. If the two distances are equal, the common distance is the radius of the circle. square root of ((-8 - -2)^2 + (7 - -1)^2) = square root of (36 + 64) = 10 square...

Depending on the style guide you use, either can be correct. Your second sentence uses the Oxford comma, which comes after the next-to-last item in a list. Sometimes the comma reduces ambiguity, as in the now famous example... I would like to thank my parents,...

Corey is 104 years old. Zoe is 24 years old. How many years until Corey's age is 3 times Zoe's age? (answer)

After adding x years to both Corey and Zoe's ages, Corey will be three times Zoe's age. (104 + x) = 3 * (24 + x) 104 + x = 72 + 3x 32 = 2x x = 16 Sixteen years from now, Corey will be 120 and Zoe will be 40.

C = Chris, J = Jorge. C = J + 11 C = 2J - 16 Since both (J + 11) and (2J - 16) are equal to C, they must also be equal to each other. J + 11 = 2J - 16 J = 27 Jorge is 27, Chris is 38. &...

The volumes of the 35% solution and 17% solution add up to 72, so the volumes of the two solutions can be expressed as x and (72-x). Volume of sugar in the 35% solution = 0.35 x. Volume of sugar in the 17% solution = 0.17 (72-x) = 12.24 - 0.17 x. You can also make...

Arithmetic Series (answer)

(x-d) + x + (x+d) = 3x = 12, so x = 4 (4-d) * 4 * (4+d) = -80 64 - 4d^2 = -80 -4d^2 = -144 d^2 = 36 d = +/- 6 The three numbers are -2, 4, and 10. The product is -80. &nb...

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